## Step 1: Define the symbolic representation of the problem
The problem involves three variables: 'milligrams of vitamin D', 'milligrams of vitamin B9', and 'milligrams of zinc'. Let's denote these as $x_0$, $x_1$, and $x_2$ respectively.

## Step 2: Translate the objective function into symbolic notation
The objective function to minimize is $3.53x_0 + 5.16x_1 + 2.52x_2$.

## 3: List the constraints in symbolic notation
1. Immune support index for $x_0$ is 5: $5x_0 \leq 198$ is not correct, it is just $5$ as a given value, not a constraint in the traditional sense but $5x_0$ represents its contribution.
2. Digestive support index for $x_0$ is 1: $1x_0$ represents its contribution.
3. Energy stability index for $x_0$ is 2: $2x_0$ represents its contribution.
4. Immune support index for $x_1$ is 6: $6x_1$ represents its contribution.
5. Digestive support index for $x_1$ is 4: $4x_1$ represents its contribution.
6. Energy stability index for $x_1$ is 7: $7x_1$ represents its contribution.
7. Immune support index for $x_2$ is 11: $11x_2$ represents its contribution.
8. Digestive support index for $x_2$ is 2: $2x_2$ represents its contribution.
9. Energy stability index for $x_2$ is 11: $11x_2$ represents its contribution.

## 4: Express given constraints
- Total immune support index from $x_1$ and $x_2$ is 36 or more: $6x_1 + 11x_2 \geq 36$.
- Total immune support index from $x_0$, $x_1$, and $x_2$ is 36 or more: $5x_0 + 6x_1 + 11x_2 \geq 36$.
- Total digestive support index from $x_0$ and $x_1$ is 44 or more: $1x_0 + 4x_1 \geq 44$.
- Total digestive support index from $x_0$, $x_1$, and $x_2$ is 44 or more: $1x_0 + 4x_1 + 2x_2 \geq 44$.
- Total energy stability index from $x_0$ and $x_1$ is 20 or more: $2x_0 + 7x_1 \geq 20$.
- Total energy stability index from $x_0$ and $x_2$ is 33 or more: $2x_0 + 11x_2 \geq 33$.
- Total energy stability index from $x_0$, $x_1$, and $x_2$ is 33 or more: $2x_0 + 7x_1 + 11x_2 \geq 33$.
- $7x_0 - 10x_2 \geq 0$.
- $9x_1 - 3x_2 \geq 0$.
- $-5x_0 + 8x_1 \geq 0$.
- Total immune support index from $x_0$ and $x_1$ is 150 or less: $5x_0 + 6x_1 \leq 150$.
- Total energy stability index from $x_0$ and $x_2$ is 164 or less: $2x_0 + 11x_2 \leq 164$.
- Total energy stability index from $x_1$ and $x_2$ is 173 or less: $7x_1 + 11x_2 \leq 173$.

## 5: Define the symbolic representation
```json
{
    'sym_variables': [
        ('x0', 'milligrams of vitamin D'),
        ('x1', 'milligrams of vitamin B9'),
        ('x2', 'milligrams of zinc')
    ],
    'objective_function': '3.53x0 + 5.16x1 + 2.52x2',
    'constraints': [
        '6x1 + 11x2 >= 36',
        '5x0 + 6x1 + 11x2 >= 36',
        'x0 + 4x1 >= 44',
        'x0 + 4x1 + 2x2 >= 44',
        '2x0 + 7x1 >= 20',
        '2x0 + 11x2 >= 33',
        '2x0 + 7x1 + 11x2 >= 33',
        '7x0 - 10x2 >= 0',
        '9x1 - 3x2 >= 0',
        '-5x0 + 8x1 >= 0',
        '5x0 + 6x1 <= 150',
        '2x0 + 11x2 <= 164',
        '7x1 + 11x2 <= 173'
    ]
}
```

## 6: Create Gurobi code
```python
import gurobi

def optimize_problem():
    model = gurobi.Model()

    # Define variables
    x0 = model.addVar(name="x0", vtype=gurobi.GRB.INTEGER)  # milligrams of vitamin D
    x1 = model.addVar(name="x1")  # milligrams of vitamin B9
    x2 = model.addVar(name="x2")  # milligrams of zinc

    # Objective function
    model.setObjective(3.53 * x0 + 5.16 * x1 + 2.52 * x2, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(6 * x1 + 11 * x2 >= 36)
    model.addConstr(5 * x0 + 6 * x1 + 11 * x2 >= 36)
    model.addConstr(x0 + 4 * x1 >= 44)
    model.addConstr(x0 + 4 * x1 + 2 * x2 >= 44)
    model.addConstr(2 * x0 + 7 * x1 >= 20)
    model.addConstr(2 * x0 + 11 * x2 >= 33)
    model.addConstr(2 * x0 + 7 * x1 + 11 * x2 >= 33)
    model.addConstr(7 * x0 - 10 * x2 >= 0)
    model.addConstr(9 * x1 - 3 * x2 >= 0)
    model.addConstr(-5 * x0 + 8 * x1 >= 0)
    model.addConstr(5 * x0 + 6 * x1 <= 150)
    model.addConstr(2 * x0 + 11 * x2 <= 164)
    model.addConstr(7 * x1 + 11 * x2 <= 173)

    # Solve the problem
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Milligrams of vitamin D: {x0.varValue}")
        print(f"Milligrams of vitamin B9: {x1.varValue}")
        print(f"Milligrams of zinc: {x2.varValue}")
        print(f"Objective function value: {model.objVal}")
    else:
        print("No optimal solution found.")

optimize_problem()
```